EXERCISE 3: THE E×B (WIEN) FILTER, PART 1

Regions of mutually perpendicular electric and magnetic fields can be used to filter a collection of moving charged particles according to their velocity. If we assume that a particle of velocity vpass=Ey/Bx enters the field region traveling exactly along the z-axis, the particle will experience zero net force and therefore zero acceleration and zero deflection from the z-axis. If a small, circular aperture of radius R is placed on the z-axis at z=L, then this particle will be transmitted through the aperture.

(a) Use your program from Exercise 2 to determine the maximum value of vz,max=vpass+Δv for which an aperture of radius R=1.0 mm will transmit the Li+ ion (now assuming that vx=vy=0). What is the value of Δv/vpass?

(b) Repeat (a) for an aperture of radius R=2.0 mm. What is the value of Δv/vpass?